Elasto-capillary circumferential buckling of soft tubes under axial loading: existence and competition with localised beading and periodic axial modes

TL;DR

This paper investigates the conditions under which soft tubes buckle circumferentially under axial load, analyzing the competition with localized beading and axial modes, and identifying regimes where circumferential buckling dominates.

Contribution

It extends previous analysis by exploring circumferential buckling modes under various boundary conditions and loads, revealing their dominance in specific regimes.

Findings

Circumferential buckling occurs under certain tensile and compressive loads.

Localised and periodic axial modes are absent in some loading regimes.

Circumferential buckling dominates over other modes in specific parameter ranges.

Abstract

We provide an extension to previous analysis of the localised beading instability of soft slender tubes under surface tension and axial stretching. The primary questions pondered here are: under what loading conditions, if any, can bifurcation into circumferential buckling modes occur, and do such solutions dominate localisation and periodic axial modes? Three distinct boundary conditions are considered; in case 1 the tube's curved surfaces are traction free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial displacement and surface tension. A linear bifurcation analysis is conducted to determine numerically the existence of circumferential mode solutions. In case 1 we focus on the tensile stress regime given the preference of slender compressed tubes towards Euler buckling over axial wrinkling. We show that tubes under several loading paths are highly sensitive to circumferential modes; in contrast, localised and periodic axial modes are absent, suggesting that the circumferential buckling is dominant by default. In case 2, circumferential mode solutions are associated with negative surface tension values and thus are physically implausible. Circumferential buckling solutions are shown to exist in case 3 for tensile and compressive axial loads, and we demonstrate for multiple loading scenarios their dominance over localisation and periodic axial modes within specific parameter regimes.